The Mach number,
,
is the ratio of the flow speed,
, to the speed of sound,
. You
will learn more about this quantity in fluids, but it is interesting
to see that
measures the ratio of the kinetic energy of the
gas to its thermal energy.

This fact is
often useful for solving thermodynamic cycles in different ways. For
instance, in this example we could sum the work terms all around the
cycle. Instead we will consider the difference between the heat
added to the cycle in process
-
, and the heat rejected by the
cycle in process
-
.

In the
above equation, and in the arguments that follow, the quantities
and
are both regarded as positive
for work done by the surroundings and heat given to the
surroundings. Although this is not in accord with the convention we
have been using, it seems to me, after writing the notes in both
ways, that doing this gives easier access to the ideas. I would be
interested in your comments on whether this perception is correct.

The transmission efficiency
represents the ratio between compressor and turbine power, which is
less than unity due to parasitic frictional effects. As with the
combustion efficiency, however, this is very close to one and the
horizontal axis can thus be regarded essentially as propulsive
efficiency.

Note: We don't need to make this assumption, and
if we were looking at the problem in detail we would solve it
numerically and not worry about whether an analytic solution
existed. In the present case, developing the analytic solution is
useful in presenting the structure of the solution as well as the
numbers, so we resort to the mild fiction of no heat transfer at the
fin end. We need to assess, after all is said and done, whether this
is appropriate or not.